A379373 Numbers k such that A050252(k) <= A055642(k).

1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 105, 106, 107, 109, 111, 112, 113, 115, 118, 119, 121, 122, 123, 125, 127, 128, 129, 131, 133, 134, 135

Offset

1,2

Comments

Some authors call these numbers "economical numbers" (see links) and refer to A046759 as "frugal numbers", while other authors define "economical numbers" to be A046759.

First differs from A046758 at n = 54, where a(54) = 125 is missing from A046758.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Richard G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.

Giovanni Resta, Economical numbers, Numbers Aplenty, 2013.

Example

112 is a term because 112 = (2^4)*7; the total number of digits of (2, 4, 7) = 1 + 1 + 1 <= the number of digits of 112 (3).
125 is a term because 125 = 5^3; the total number of digits of (5, 3) = 1 + 1 <= the number of digits of 125 (3).

Mathematica

A379373Q[k_] := Total[IntegerLength[Select[Flatten[FactorInteger[k]], # > 1 &]]] <= IntegerLength[k];
Select[Range[200], A379373Q]

Prog

(Python)
from sympy import factorint
def ok(n): return n > 0 and sum(len(str(p))+(len(str(e)) if e>1 else 0) for p, e in factorint(n).items()) <= len(str(n))
print([k for k in range(136) if ok(k)]) # Michael S. Branicky, Dec 22 2024

Crossrefs

Union of A046758 and A046759.

Complement of A046760.

Cf. A050252, A055642.

Sequence in context: A267521 A202267 A125975 * A046758 A121232 A298746

Adjacent sequences: A379370 A379371 A379372 * A379374 A379375 A379376

Keyword

nonn,base,new

Author

Paolo Xausa, Dec 21 2024

Status

approved